Question 24
In a row are six counters, each either black or white. Between every two adjacent counters, we place a new counter. If the two adjacent counters are of the same colour, we place a white counter. If they are of different colours, we place a black counter. Then we remove the original six counters, leaving behind a row of five counters. We now repeat this operation two more times, reducing the number of counters in the row to four and then to three. If the last three counters are all white, how many different colour patterns for the original six counters are there? An example is attached.
